Is there a methodology for splitting up annotated orthophotos into smaller photos that retain the original bounding boxes?
You can reduce your photo size and scale the corresponding boxes to the new dimensions (416x416).
Or if you want to go with your technique, you can slice the image and then, check if the bounding box lies in the slice, then, reorient it according to the slice you took.
Take a look at albumentations library for this.